🧮 algebra

1. **State the problem:** Evaluate the expressions given the values $x = -2$, $y = -3$, and $z = -2$. 2. **Part a) Calculate $xyz$:**

1. **State the problem:** Factorize the quadratic expression $6x^2 + 19x + 15$. 2. **Identify coefficients:** Here, $a=6$, $b=19$, and $c=15$.

1. The problem is to convert the expression $$(x+2)^2 - \frac{4}{3}$$ into standard form. 2. Start by expanding the squared term using the formula $$(a+b)^2 = a^2 + 2ab + b^2$$:

1. **State the problem:** We have four digits 3, 5, 7, 8 to fill in the missing places in two decimal numbers on a number line between 7 and 9. The numbers are of the form $[\_].7[

1. The problem is to find the square root of 1538, written as $\sqrt{1538}$.\n\n2. First, estimate the value by finding perfect squares near 1538.\n\n3. Note that $39^2 = 1521$ and

1. **State the problem:** We have the value of an antique sewing table given by the function $$V = 1200(1.06)^t$$ where $V$ is the value in dollars and $t$ is the time in years. We

1. The problem is to find the square root of 1539, written as $\sqrt{1539}$.\n\n2. First, check if 1539 is a perfect square by finding factors or estimating.\n\n3. Estimate: $39^2

1. Let's start by stating the problem clearly: you want to solve an equation using an algebraic formula. 2. Since you did not specify the exact equation, I will demonstrate solving

1. The problem is to solve a quadratic equation without using the algebraic formula (quadratic formula). 2. Instead, we can use factoring, completing the square, or graphing method

1. **Problem statement:** Find the products of the expressions: i) $ (a - 1)(a^2 + a + 1) $

1. **State the problem:** We need to show that $$-11100 \times 134 \equiv -1 \pmod{13}$$ without using a calculator. 2. **Reduce each number modulo 13:**

1. **Solve the system of equations:** Given:

1. The problem states that the cost $C$ of renting the yacht depends on the number of people $p$ in the group. 2. The cost per person is 75, and there is a fixed rental fee of 350.

1. The problem is to factorize the given equation. However, the equation itself is not provided. 2. To factorize an equation, we need the specific polynomial or expression.

1. The problem is to factor the quadratic expression $6x^2 + 14x + 15$. 2. First, identify coefficients: $a=6$, $b=14$, and $c=15$.

1. The problem asks us to identify the independent and dependent variables from the graph of the valve on the bike tire and to state the domain and range. 2. The independent variab

1. **State the problem:** We have the formula for the number of blades of grass on a fertilized lawn as $$B = 48l \pm 2$$ where $B$ is the number of blades and $l$ is the area of t

1. **State the problem:** Solve the equation $$\frac{1}{x} + \frac{1}{2x} = 3$$ for $x$. 2. **Find a common denominator:** The denominators are $x$ and $2x$. The least common denom

1. The problem is to simplify the expression: $$\frac{1}{3} \times \frac{5}{1} - 2x \times \frac{7}{1} \times \frac{1}{2}$$. 2. First, multiply the fractions in the first term:

1. The problem is to rearrange the equation $$2y = \sqrt{x + 3} + 2$$ to make $$x$$ the subject. 2. Start by isolating the square root term on one side:

1. We are asked to factor the cubic polynomial $2x^3 + 9x^2 - 6x - 5$. 2. First, try to find rational roots using the Rational Root Theorem. Possible roots are factors of the const